Partial euler characteristic, normal generations and the stable D(2) problem

We study the interplay amongWall's D(2) problem, the normal generation conjecture (the Wiegold Conjecture) of perfect groups and Swan's problem on partial Euler characteristic and deficiency of groups. In particular, for a 3-dimensional complex X of cohomological dimension 2 with finite fundamental group, assuming the Wiegold conjecture holds, we prove that X is homotopy equivalent to a finite 2-complex after wedging a copy of sphere S².